The Vector Equilibrium (VE) (a.k.a. cuboctahedron) has 4 *goups*
of spin axes. These are

- 4 triangle face-center-to-face-center axes
- 3 square face-center-to-face-center axes
- 6 vertex-to-vertex axes
- 12 midedge-to-mid-edge axes

Below I show which axis *group* grenerates which great circle
arcs across the VE's faces. The bold arcs are generated by the
associated axis group as labeled.

The surface of the spherical VE can be covered by 24 "positive" and 24 "negative" (total = 48) spherical triangles known as the VE LCD spherical triangle. This is the spherical triangle shown in bold in the illustration below.

Now for the tables of the spherical VE's LCD spherical triangle angles.

All angles are given in degrees.

LABEL | ANGLE | Q.M.Equ. |
---|---|---|

BAC | 30.000 000 000 | acos(3,3) |

CAD | 30.000 000 000 | acos(3,3) |

ABC | 90.000 000 000 | acos(0,1) |

CBE | 90.000 000 000 | acos(0,1) |

ACB | 61.874 494 298 | acos(4,8) |

ACD | 118.125 505 702 | 180-acos(4,8) |

BCF | 118.125 505 702 | 180-acos(4,8) |

DCF | 61.874 494 298 | acos(4,8) |

ADC | 35.264 389 683 | acos(2,2) |

CDF | 19.471 220 634 | acos(8,8) |

FDG | 35.264 389 683 | acos(2,2) |

BEF | 73.221 345 119 | acos(1,3) |

FEG | 33.557 309 762 | asin(55,99) |

GEH | 73.221 345 119 | acos(1,3) |

CFD | 99.594 068 227 | 90+acos(35,35) |

CFE | 80.405 931 773 | asin(35,35) |

DFG | 80.405 931 773 | asin(35,35) |

EFG | 99.594 068 227 | 90+acos(35,35) |

DGF | 65.905 157 448 | acos(1,2) |

EGF | 48.189 685 104 | asin(60,80) |

EGH | 65.905 157 448 | acos(1,2) |

EHG | 45.000 000 000 | acos(1,1) |

LABEL | ANGLE | Q.M.Equ. |
---|---|---|

AB | 19.471 220 634 | acos(8,8) |

AC | 22.207 654 299 | acos(6,6) |

AD | 35.264 389 683 | acos(2,2) |

BC | 10.893 394 649 | acos(27,27) |

BE | 10.024 987 862 | asin(2,11) |

CD | 19.106 605 351 | asin(9,27) |

CF | 6.353 170 919 | |

DF | 17.023 866 185 | asin(6,20) |

DG | 18.434 948 823 | acos(9,9) |

EF | 14.458 287 920 | |

EG | 19.286 325 411 | acos(42,44) |

EH | 25.239 401 821 | acos(4.5,4.5) |

FG | 10.670 695 266 | |

GH | 26.565 051 177 | acos(4,4) |

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